Flutter of high-dimension nonlinear system for a FGM truncated conical shell

ABSTRACT

The nonlinear flutters of a truncated conical shell, which is subjected to aerodynamic pressure and aerodynamic heating, are researched. Material properties with gradient features along the radial direction depend on the temperature. The supersonic aerodynamic force is obtained by applying the first-order piston theory, including the correction factor for curvature. The temperature in the external surface of the functionally graded material truncated conical shell rises as a result of viscous aerodynamic heating, and the temperature distribution along the thickness can be described by polynomial series. Hamilton's principle is utilized to obtain the nonlinear partial differential equilibrium equation of the system. Using Galerkin's method, a high-dimensional nonlinear system can be derived. Without considering the parts of nonlinear terms and the external forcing excitation, the flutter boundaries are obtained by solving the eigenvalues problem. The influences of ratios of top radius to thickness, semi-vertex angle, and volume fraction index on nonlinear dynamic characteristics of functionally graded material truncated conical shell are studied in detail by the fourth-order Runge–Kutta algorithm.

KEYWORDS:

• Flutter boundary
• functionally graded materials
• high dimension
• nonlinear dynamics
• truncated conical shell

Funding

The authors acknowledge the financial support of National Natural Science Foundation of China through grant No. 11272063 and 11290152.